Disclaimer: My knowledge of "priesthood of all believers" is limited, what I write always reflects my understanding of the general doctrine and may differ between denominations.
Priesthood of all believers (as far as I understand):
All believers have the priesthood, meaning they can, for example baptise. No ordination required, the authority comes from the Holy Ghost.
Priesthood is conferred by ordination of someone holding authority to do so (another priesthood holder). All worthy men may receive the priesthood, and are encouraged to do so. Priesthood also entails a convenant with God. Many priesthood holders have a list that traces back who ordained whom and can trace back their priesthood to Joseph Smith (and then, through Joseph Smith, to Peter, James and John and ultimately Jesus Christ himself).
Duty and service
Priesthood of all believers
While all lay people are priests, most congregations have professional ministers. Other functions are filled by the members of the congregation. Degree of central organization differs. Lutherans are very organized, Evangelicals supposedly less so. Since everyone is a priest, it is unclear if the priesthood entails any duties.
The priesthood entails well-defined duties (notably the ones in D&C 20) which express themselves in the congregational life, for example that every priesthood holder (except deacons) gets the responsibility to regularly visit and care for a number of member families (home teaching). The priesthood is also the reason why a mission is expected of a young adult man, but not of women (which can still go but don't share the same duty).
Everyone is serving in the church one way or another, the specific calling is given by the leadership (the bishop in case of a ward calling), and understood to be inspired. With the exception of Apostles, all callings end after a few years, at which point the person is assigned a different calling. Everyone is lay, including bishops and all higher positions. Anecdotally, my different bishops' professions over the years have included everything from bus driver to university professor.
So, the similarity is certainly that almost all men encountered in the church are priesthood holders. The difference is where the authority to act in God's name (the priesthood) is coming from. Churches which believe in "priesthood of all believers" derive their priesthood from the Holy Ghost. LDS believe that this is not enough, it must be transferred from someone that already has the authority to act in God's name.